Wrapped M5-branes, consistent truncations and AdS/CMT

At the level of the bosonic fields, we construct consistent Kaluza–Klein reductions of D = 11 supergravity on Σ3 × S, where Σ3 = H/Γ, S/Γ or R/Γ where Γ is a discrete group of isometries. The result is the bosonic content of an N = 2 D = 4 gauged supergravity with a single vector multiplet and two hypermultiplets, whose scalar fields parametrise SU(1, 1)/U(1)×G2(2)/SO(4). When Σ3 = H/Γ the D = 4 theory has an AdS4 vacuum which uplifts to the known supersymmetric AdS4×H/Γ× S solution of D = 11 supergravity that describes the N = 2 d = 3 SCFT arising when M5-branes wrap SLag 3-cycles H/Γ in Calabi-Yau three-folds. We use the KK reduction for Σ3 = H /Γ to construct D = 11 black hole solutions that describe these d = 3 SCFTs at finite temperature and charge density and show that there is a superconducting instability involving charged scalar fields, and another instability involving neutral fields. We also use this KK reduction to construct a D = 11 Lifshitz solution that is dual to a d = 3 field theory with dynamical exponent z ∼ 39.